The effects produced by the occurrence of both ideal and resistive instabilities in magnetohydrodynamic (MHD) turbulence are discussed, from the point of view of the formation of coherent structures. It is shown that MHD equations spontaneously develop spatially flat or elongated structures, a fact that might be related with the intermittency of the magnetic field observed in some numerical simulations. It is suggested that these flat structures are perhaps unstable with respect to reconnecting (tearing mode type) perturbations. Such instabilities give rise to a nonlocal energy transfer in the wave number space, which modifies the usual inertial spectrum of MHD turbulence, and increases the rate of energy and correlation dissipation. An explicit nonlinear cascade model that qualitatively takes into account such a nonlocal energy transfer is built up, in order to study dynamically the balance between nonlinear energy cascade and linear tearing mode instability. Finally, an attempt is made to interpret some of the peculiar behavior of published MHD simulations on the basis of the results obtained using the present model.